In this subsection, we assume that the Upstairs Unipotent Stabiliser Assumption REF  holds, but the Upstairs Reductive Stabiliser Assumption REF  does not. Our approach will be to reduce to the case where both REF  and REF  hold by performing an equivariant blow-up sequence which involves considering dimensions of stabilisers for the action of the reductive group \(R\)  on \(X\)  analogous to the reductive partial desingularisation procedure [1]} outlined in \(§\)REF .
